André Villas-Boas urged Tottenham Hotspur's supporters to "keep the faith" after his team surrendered the initiative to Arsenal in the pursuit of Champions League qualification despite twice coming from behind to frustrate Chelsea.

The stalemate, secured by Gylfi Sigurdsson's late equaliser, left Spurs a point off fourth place with two games to play. Their manager, making his first visit to the club that had sacked him in March 2012 after only 256 days in charge, was left to hope their London rivals drop points in what remains of the campaign.

"Anything can happen," he said. "The Premier League is completely unpredictable and the next fixtures, with the emotion of the last few games of the season, can be decisive. Keep the faith. Our situation has changed because destiny is not in our hands, but all we can do is win the next two fixtures [against Stoke and Sunderland] and hope somebody slips up. I'm still extremely pleased by the performance.

"It was a great example of Tottenham's determination and ambition. We increased the tempo and played really well: it was difficult to control Chelsea's creativity but we had attacking strength and created our own chances. Our focus is on us doing our job in the remaining fixtures and in the Premier League anything can happen. Keep the faith."

Those sentiments were echoed by his players after the late equaliser meant Tottenham, despite only three wins in eight games, have secured 14 points in the last 10 minutes of games since the turn of the year. "We showed fighting spirit again," said Michael Dawson. "Okay, the top four is out of our hands, but someone might do us a favour when they play Arsenal. The draw keeps things going."

Villas-Boas hopes to have Mousa Dembélé restored to fitness after a thigh injury in time for their game at the Britannia Stadium on Sunday.

Chelsea, too, still have work to do if they are to secure their top-four finish, though a victory against either Aston Villa or Everton in their remaining games will be enough given their superior goal difference over Spurs. Even so, Rafael Benítez's frustration was clear with this a missed opportunity to secure the required points. Chances were passed up, most notably when Ramires slipped when well placed to score the home side's third, to leave the Spaniard admitting fatigue had played its part in his side's late toils. This game was their 66th of a draining campaign.

"We didn't have the legs," said the interim first-team manager. "Their second goal was offside but still, we had to defend it better. At the end we were a little bit leggy and were too open, and they were pushing and attacking, and our final pass was a problem.

"We had some players tired, especially in the wide areas controlling their full-backs. We couldn't hold the ball, so it was not easy. But we had to finish the game off. They pushed and pushed, that's fine, but we had to find that third. We had chances on the counterattack to score the third goal, but there was no finish."

The manager's decision to substitute Oscar for Yossi Benayoun six minutes from time provoked a chorus of boos from the home support, the disaffection apparently aimed more at Benítez. John Terry later apologised to the Israeli player on behalf of the club for his vitriolic reception.

"I just concentrate on my football," said Benítez, when asked about the fans' reaction. "We were weak in the wide areas and a bit tired, and I didn't see any other wingers on the bench to rectify this. That was my idea [for the substitution]."